Driving is a complex task, which can be broken down into specific cognitive processes. In order to determine which components contribute to drowsy driving impairments, the current study examined simulated driving and neurocognitive performance after one night of sleep deprivation. Nineteen professional drivers (age 45.3 ± 9.1) underwent two experimental sessions in randomised order: one after normal sleep and one after 27 h total sleep deprivation. A simulated driving task (AusEd), the psychomotor vigilance test (PVT), and neurocognitive tasks selected from the Cognitive Drug Research computerised neurocognitive assessment battery (simple and choice RT, Stroop Task, Digit Symbol Substitution Task, and Digit Vigilance Task) were administered at 10:00 h in both sessions. Mixed-effects ANOVAs were performed to examine the effect of sleep deprivation versus normal sleep on performance measures. To determine if any neurocognitive tests predicted driving performance (lane position variability, speed variability, braking RT), neurocognitive measures that were significantly affected by sleep deprivation were then added as a covariate to the ANOVAs for driving performance. Simulated driving performance and neurocognitive measures of vigilance and reaction time were impaired after sleep deprivation (p < 0.05), whereas tasks examining processing speed and executive functioning were not significantly affected by sleep loss. PVT performance significantly predicted specific aspects of simulated driving performance. Thus, psychomotor vigilance impairment may be a key cognitive component of driving impairment when sleep deprived. The generalisability of this finding to real-world driving remains to be investigated.